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Some Measurability Results for Extrema of Random Functions Over Random Sets

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  • Maxwell B. Stinchcombe
  • Halbert White

Abstract

We consider the question, "Under what conditions is the extremum of a random function over a random set itself a random object?" The answer is relevant to problems in both game theory and econometrics, as we illustrate with examples. Our purpose here is to bring the powerful tools of the theory of analytic sets as developed by Dellacherie and Meyer (1978) to the wider attention of the economics profession and to distill Dellacherie and Meyer's work in such a way as to provide some readily accessible theoretical results that will permit relatively easy treatment of economically or econometrically relevant applications.

Suggested Citation

  • Maxwell B. Stinchcombe & Halbert White, 1992. "Some Measurability Results for Extrema of Random Functions Over Random Sets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(3), pages 495-514.
    • Handle: RePEc:oup:restud:v:59:y:1992:i:3:p:495-514.
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    File URL: http://hdl.handle.net/10.2307/2297861
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    Cited by:

    1. Dufour, Jean-Marie, 2006. "Monte Carlo tests with nuisance parameters: A general approach to finite-sample inference and nonstandard asymptotics," Journal of Econometrics, Elsevier, vol. 133(2), pages 443-477, August.
    2. Preminger, Arie & Storti, Giuseppe, 2014. "Least squares estimation for GARCH (1,1) model with heavy tailed errors," MPRA Paper 59082, University Library of Munich, Germany.
    3. Santos, Andres, 2011. "Instrumental variable methods for recovering continuous linear functionals," Journal of Econometrics, Elsevier, vol. 161(2), pages 129-146, April.
    4. Jin Seo Cho & Peter C. B. Phillips & Juwon Seo, 2019. "Parametric Inference on the Mean of Functional Data Applied to Lifetime Income Curves," Working papers 2019rwp-153, Yonsei University, Yonsei Economics Research Institute.
    5. Tabri, Rami Victor, 2014. "Testing for normality in linear regression models using regression and scale equivariant estimators," Economics Letters, Elsevier, vol. 122(2), pages 192-196.
    6. Jin Seo Cho & Peter C. B. Phillips & Juwon Seo, 2022. "Parametric Conditional Mean Inference With Functional Data Applied To Lifetime Income Curves," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(1), pages 391-456, February.
    7. Sakata, Shinichi & White, Halbert, 2001. "S-estimation of nonlinear regression models with dependent and heterogeneous observations," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 5-72, July.
    8. Chen, Yi-Chun & Kunimoto, Takashi & Sun, Yifei & Xiong, Siyang, 2022. "Maskin meets Abreu and Matsushima," Theoretical Economics, Econometric Society, vol. 17(4), November.
    9. Banks, Jeffrey S. & Duggan, John & Le Breton, Michel, 2002. "Bounds for Mixed Strategy Equilibria and the Spatial Model of Elections," Journal of Economic Theory, Elsevier, vol. 103(1), pages 88-105, March.
    10. Patrick Minford & Konstantinos Theodoridis & David Meenagh, 2009. "Testing a Model of the UK by the Method of Indirect Inference," Open Economies Review, Springer, vol. 20(2), pages 265-291, April.
    11. Mathias Mørck Ljungdahl & Mark Podolskij, 2020. "A minimal contrast estimator for the linear fractional stable motion," Statistical Inference for Stochastic Processes, Springer, vol. 23(2), pages 381-413, July.
    12. Kaido, Hiroaki & White, Halbert, 2014. "A two-stage procedure for partially identified models," Journal of Econometrics, Elsevier, vol. 182(1), pages 5-13.
    13. Stinchcombe, Maxwell B., 2016. "Objective and subjective foundations for multiple priors," Journal of Economic Theory, Elsevier, vol. 165(C), pages 263-291.
    14. Mathias Mørck Ljungdahl & Mark Podolskij, 2022. "Multidimensional parameter estimation of heavy‐tailed moving averages," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 593-624, June.
    15. Kemp, Gordon C.R., 2020. "Uniform convergence in extended probability of sub-gradients of convex functions," Economics Letters, Elsevier, vol. 188(C).
    16. Beare, Brendan K., 2009. "Distributional Replication," University of California at San Diego, Economics Working Paper Series qt65k3m6x9, Department of Economics, UC San Diego.
    17. Mr. Kenichi Ueda, 2001. "Transitional Growth with Increasing Inequality and Financial Deepening," IMF Working Papers 2001/108, International Monetary Fund.
    18. Ueda, Kenichi, 2013. "Banks as coordinators of economic growth and stability: Microfoundation for macroeconomy with externality," Journal of Economic Theory, Elsevier, vol. 148(1), pages 322-352.
    19. Jin Seo Cho & Meng Huang & Halbert White, 2021. "Testing a Constant Mean Function Using Functional Regression," Working papers 2021rwp-190, Yonsei University, Yonsei Economics Research Institute.
    20. Jin Seo Cho & Meng Huang & Halbert White, 2009. "Testing for a Constant Mean Function using Functional Regression," Discussion Paper Series 0915, Institute of Economic Research, Korea University.
    21. Thomas M. Russell, 2020. "Policy Transforms and Learning Optimal Policies," Papers 2012.11046, arXiv.org.

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